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Question

The inverse of f(x)=(5āˆ’(xāˆ’8)5)13 is


A

5(x8)5

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B

8+(5x3)15

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C

8(5x3)15

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D

(5(x8)15)3

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Solution

The correct option is B

8+(5x3)15


y=f(x)=(5(x8)5)13
then y3=5(x8)5(x8)5=5y3
x=8+(5y3)15
Let, z=g(x)=8+(5x3)15
To check, f(g(x))= [5(x8)5]13
=(5[(5x3)15]5)13=(55+x3)13=x
similarly , we can show that g(f(x))=x
Hence, g(x)=8+(5x3)15 is the inverse of f(x)


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